Related papers: Generalized heat-transport equations: Parabolic an…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time…
The heat equation, based on Fourier's law, is commonly used for description of heat conduction. However, Fourier's law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short…
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results…
Heat transport exhibits distinct regimes ranging from ballistic propagation to diffusive relaxation, traditionally described by disparate theoretical frameworks. Here, we introduce a unified first-order operator formulation in which…
We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
Relativistic thermodynamics is constructed from the point of view of special relativistic hydrodynamics. A relativistic four-current for heat and a general treatment of thermal equilibrium between moving bodies is presented. The different…
I will discuss, from a dynamical systems point of view, some recent attempts to rigorously derive the macroscopic laws of transport (e.g. the heat equation) from deterministic microscopic dynamics.
We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.
The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at…
We investigate the relaxation dynamics of heat transport in superconductors, shaped by the interplay of diffusion, nonlinearity, and magnetic fields. Focusing on regimes near the critical temperature Tc, we analyze two classes of relaxation…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
The fundamental dynamic stability of heat conduction theories beyond Fourier is analyzed in the framework of nonequilibrium thermodynamics. It is shown, that the thermodynamic framework, concave entropy and nonnegative entropy production,…
Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported.…
The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and non-equilibrium thermodynamics. The governing equations of irreversible…
We consider the coupling between the equations of motion of a compressible fluid in two and three space dimensions with Christov's equation for the heat flux. Christov's equation is a frame indifferent formulation of the classical model of…
The present work deals with irreversible Universal thermodynamics. The homogenous and isotropic flat model of the universe is chosen as open thermodynamical system and non-equilibrium thermodynamics comes into picture due to the mechanism…